Solving the following inequalities. Give both inequality and interval notation forms of the solution.
-2 ( m - 3) < 5 ( m + 1) -12
Solution
Solving out single linear inequalities follow pretty much the similar process for solving linear equations. We will simplify both of the sides, get all the terms along with the variable on one side & the numbers on the other side, & then multiply/divide both of sides through the coefficient of the variable to obtain the solution. The one thing which you've got to recall is that if you multiply/divide by a negative number then switches the direction of the inequality.
Really there isn't much to do here other than follow the procedure outlined above.
-2 (m - 3) < 5 ( m + 1) -12
-2m + 6 < 5m + 5 -12
-7m < -13
m < 13/ 7
You did notice the fact that the direction of the inequality vary here didn't you? We divided by a "-7" and thus we had to change the direction. The inequality form of the solution is m > 7.
The interval notation for this solution is, ( 13/ 7, ∞ ) .